SAW devices are successfully used in wireless communication systems as a result of their small size and low insertion loss, which is provided by a resonator-type structure, built on piezoelectric substrates with high electromechanical coupling. Such devices commonly utilize low-attenuated quasi-bulk leaky surface acoustic waves (LSAW) characterized by high electromechanical coupling coefficient. Such waves are known to exist in two piezoelectric crystals, lithium tantalate, LiTaO3 (LT), and lithium niobate, LiNbO3 (LN), by way of example.
Both crystals are oxide ferroelectrics with anti-parallel domain structure and belong to the point symmetry class 3 m. The same symmetry and domain structure determines many common features typical for these two crystals, first of all strong piezoelectric effect. The same type of surface acoustic waves propagates along X-axis in rotated Y-cuts of two crystals (in SAW literature, such orientations are also called ‘rotated YX-cuts’). This type of waves is characterized by quasi-SH (shear horizontal) polarization and can be considered as the fast shear bulk wave modified by anisotropy, piezoelectric effect and mass load produced by an electrode pattern of a resonator structure. Leaky waves degenerate into a pure SH-polarized bulk wave in one particular orientation, close to 37° YX cut in LT and close to 41° YX cut on LN, if the effects of electrical boundary conditions and mass load are ignored.
Due to the quasi-bulk structure of the aforementioned type of leaky waves, the electromechanical coupling coefficient, which characterizes piezoelectric efficiency of SAW radiation and determines maximum bandwidth (BWmax) of SAW devices utilizing these waves, can be nearly as high as the coupling of bulk waves. As substrates of SAW devices with resonator structures, 36° YX-48° YX cuts of LT and 41° YX-76° YX cuts of LN are commonly used. The characteristics of leaky waves propagating in these orientations were reported by Naumenko and Abbott (in Proc. 2002 IEEE Ultrasonics Symposium, pp 385-390 and in Proc. 2003 IEEE Ultrasonics Symposium, pp. 2110-2113).
The performance characteristics of a SAW filter utilizing leaky waves depend on attenuation (propagation loss) caused by radiation of bulk acoustic waves accompanying LSAW propagation. Low attenuation of LSAW is necessary to provide low insertion loss in SAW filters. An attenuation coefficient is an anisotropic parameter. Therefore, it can be minimized by using optimal orientation of piezoelectric crystal as a substrate. On the other side, the attenuation coefficient is a frequency-dependent parameter, which means that it can be minimized only at fixed frequency and can grow significantly with deviation from this specific frequency. For example, the propagation loss can be minimized at the frequency located at the lower edge of the resonator Bragg's stopband. If an electrical boundary condition in a resonator structure is short-circuited (SC), the lower edge of the stopband usually coincides with a resonant frequency. With an open-circuit (OC) electrical boundary condition, it usually coincides with anti-resonant frequency. U.S. Pat. No. 6,661,313 and U.S. Pat. No. 6,556,104, the disclosures of which are herein incorporated by reference in their entirety, teach that when the propagation loss is minimized at the frequency located in the middle between resonance and anti-resonance, in addition to low insertion loss, the shape factor of the resonator filter can be improved. With such an optimization criterion, the optimal dependences between electrode thickness and rotation angle were determined in the aforementioned patents, respectively, for rotated YX-cuts of LT and rotated YX-cuts of LN.
By way of example, reference is made to FIG. 1 illustrating the intervals in which the values of a squared electromechanical coupling coefficient k2 are confined for rotated YX-cuts of LT and LN, if electrode thickness is optimized to provide average propagation loss lower than 0.02 dB/λ or lower than 0.05 dB/λ. In 36° YX-48° YX cuts of LT, these intervals are k2=(7.3-8.2) % and k2=(7-9.5) %, respectively. In 41° YX-76° YX cuts of LN, the corresponding intervals are k2=(11-17.5) % and k2=(9-18) %, respectively. Such values of electromechanical coupling coefficients are sufficient to build resonator SAW filters with maximum bandwidths between 3 and 8%. The choice of material of a substrate and particular orientation depends on a required bandpass width of SAW filter.
Another characteristic of the wave which affects the choice of a substrate material and orientation for SAW device is Temperature Coefficient of Frequency (TCF), which determines stability of the main parameters of SAW filter to variation of temperature. For leaky waves propagating in aforementioned orientations, TCF varies between 30 ppm/° C. and 40 ppm/° C. for rotated Y-cuts of LT and between 60 ppm/° C. and 80 ppm/° C. for rotated Y-cuts of LN, dependent on orientation and electrical boundary condition. The temperature characteristic of SAW filter can be improved if a thin isotropic film of dielectric material with positive TCF, such as silicon dioxide, SiOx, is disposed on the substrate, over the resonator structures. Due to the opposite signs of TCF in the substrate and overlay materials, small or even zero absolute values of the TCF can be obtained in such devices.
As described in M. Kadota, in Proc. Ultrasonic Symposium 2007, pp. 496-506, Kadota reports the type of layered structure, which combines LT or LN substrate with a SiOx overlay and can be utilized in resonator-type filters with improved temperature characteristics. To provide high electromechanical coupling factor in such devices, the surface of SiOx film is preferably flattened, as illustrated in FIG. 2, and as will be described in greater detail for a description of embodiments. In addition, to provide efficient reflection of SAW from the resonator structure, the electrodes of resonator-type elements are made of material with density higher than the density of aluminum. For example, copper (Cu) can be used as a primary component of electrode material. Kadota shows that the absolute value of the TCF about 10 ppm/° C. or less can be obtained in SAW devices built on LT or LN substrate with Cu electrodes and SiOx overlay when the thickness of SiOx overlay is about 40-60% of LSAW wavelength.
Deposition of SiOx film over the resonator-type elements of SAW filter changes all leaky wave characteristics, including attenuation. The optimal combination of orientation and electrode thickness, which provides minimum attenuation of leaky wave, depends on SiOx film thickness. By way of example, FIG. 3 illustrates an average propagation loss estimated in the middle between resonant and anti-resonant frequencies, as function of Cu electrode thickness, in three orientations of LT, 36° YX, 42° YX and 48° YX cuts. The effect of SiOx film on the characteristics of LSAW propagating in these orientations was simulated assuming that SiOx film can be adequately characterized by material constants as reported by H. Nakahata et al., in Proc. Ultrasonic Symposium, 1995, pp. 361-370 (Nakahata), and material constants of LT and LN are consistent with the values reported by Kushibiki in IEEE Trans. Ultrason., Ferroelect., Freq. Contr., 1999, v. 46, pp. 1315-1323 (Kushibiki). The characteristics of LSAW obtained with the material constants mentioned above are consistent with experimental LSAW characteristics measured by Kadota, as will be described later.
From FIG. 3, it is clear that without the SiOx film, a minimum propagation loss is expected in 42° YX and 48° YX cuts, respectively, at the normalized electrode thicknesses 1.7% λ and 3.8% λ, where λ=2p is a wavelength at synchronous resonance condition, and p is periodicity of electrode structure. If SiOx is disposed between electrodes of resonator structures, with flattened top surface of the whole structure, then the optimal values of electrode thickness, which provide minimum propagation losses, move to 2.5% λ and 5.8% λ, respectively. With deposition of additional SiOx overlay on top of this structure, the optimal electrode thickness changes and further deviates from the initial electrode thicknesses providing minimum propagation loss without SiOx overlay.
Thus, optimization is required for each SiOx film thickness, by means of variation of cut angle and electrode thickness. In U.S. Pat. No. 6,836,196 to Kadota et al., an example of such optimization is presented, reference being made to FIG. 17 of the Kodota patent. The optimal rotation angles were found for rotated YX-cuts of LT, as functions of SiOx film thickness, at Cu electrode thicknesses 2% λ, 4% λ, 6% λ and 8% λ, in order to minimize propagation loss at resonant frequency. The main disadvantage of such optimization is that it is unable to provide low propagation loss in the middle and at the high-frequency edge of resonator Bragg's stopband and in the middle of filter passband. Moreover, asymmetry of the attenuation coefficient, with respect to the center of the stopband, may cause additional distortion of the frequency characteristic and degradation of steepness (shape factor) at the high-frequency edge of filter passband.
FIG. 4 illustrates how the propagation losses, estimated at resonant and anti-resonant frequencies, depend on electrode thickness, in 42° YX cut of LT with Cu as electrode material. Without a SiOx overlay, simultaneously low propagation losses, about 0.002 dB/λ, are expected at resonant and anti-resonant frequencies if electrode thickness is about 1.8% λ. With a SiOx film having thickness hSiOx=10% λ (the thickness of SiOx overlay is measured on top of electrode, as shown in FIG. 1), the optimal electrode thickness increases to hCu=2.95% λ, and the minimum average propagation loss grows up to 0.006 dB/λ. However, this minimum propagation loss can be decreased if the cut angle is adjusted with SiOx film thickness, by means of simultaneous variation of cut angle and electrode thickness.
FIG. 5 and FIG. 6 include contour plots of propagation losses of leaky waves in rotated YX-cuts of LT, at resonant and anti-resonant frequencies, respectively. The propagation losses were evaluated as functions of rotation angle and normalized electrode thickness, for LT substrates with resonators comprising Cu electrodes and SiOx overlay, when hSiOx=20% λ. In the shaded area, which was reported as optimal area by Kadota (U.S. Pat. No. 6,836,196), the propagation loss estimated at resonant frequency is less than 0.005 dB/λ. See FIG. 5. However, at anti-resonant frequency (see FIG. 6), attenuation in the shaded area exceeds 0.04 dB/λ, which is much higher than at resonant frequency. This will cause asymmetric distortion of frequency characteristics of the SAW filter and hence general degradation of filter performance.
To overcome the disadvantage caused by asymmetry of propagation loss in the resonator stopband, U.S. Pat. No. 7,212,080 to Mimura et al. (Mimura) investigated Q-factors of LSAW resonator at resonant and anti-resonant frequencies, as functions of cut angle, in rotated YX-cuts of LT, at fixed thickness of Cu electrodes, about 4% λ, and fixed thickness of SiOx film, about 20% λ. Mimura discloses that propagation loss is simultaneously minimized at resonant and anti-resonant frequencies if such resonator structure is built on orientation close to 45° YX cut of LT. However, Mimura does not show how this optimal orientation changes with variation of Cu and SiOx film thicknesses, though such variation is required to build resonator filters with different passband widths and improved TCF. The dependencies between the optimal cut angles, in rotated YX-cuts of LT and LN, and thicknesses of electrodes and SiOx film overlay are strongly required to build low-loss resonator filters with improved performance, improved temperature characteristics and wide range of passband widths.